[seqfan] Array where a permutation of the primes produces all non-primes

[Eric Angelini]

Hello SeqFans,
Jean-Marc Falcoz has computed 60 terms of the first line hereunder,
-- and the resulting array. The constraints were:
1) the first line of the array must be a permutation of the primes;
2) the array, seen as a whole, must be a permutation of the naturals;
3) any two neighboring integers have their absolute first difference
   written on the line below, between them.

2  3   13  47   197   11  29   443  397   1321  4831   15559    211     5      19    41   293   113   971 ...
  1  10  34  150  186   18  414   46   924   3510  10728   15348    206    14     22   252   180   858 ...
    9  24  116  36   168  396  368  878   2586  7218    4620   15142    192     8    230   72   678 ...
     15  92   80  132   228   28  510  1708   4632  2598   10522   14950    184   222   158  606 ...
       77   12  52    96   200  482 1198  2924   2034   7924    4428   14766    38    64   448 ...
          65  40   44   104  282  716  1726   890   5890    3496   10338   14728   26   384 ...
            25   4    60   178  434 1010   836   5000   2394    6842   4390    14702  358 ...
               21  56   118   256 576   174   4164   2606   4448   2452   10312   14344 ...
                 35   62   138   320  402  3990  1558   1842    1996   7860    4032  ...
                    27   76   182   82  3588  2432   284    154    5864    3828 ...
                      49   106  100  3506  1156  2148    130    5710   2036 ...
                         57   6   3406  2350   992   2018   5580   3674 ...
                           51  3400  1056  1358  1026   3562   1906 ...
                            3349   2344  302  332    2536  1656 ...
                               1005   2042  30    2204   880 ...
                                   1037  2012  2174  1324 ...
                                      975   162   850 ...
                                         813   688 ...
                                            125 ...

After 60 terms (first line), the smallest missing prime is 17 and
the smallest missing non-prime is 39.

The first line is the lexicographically first one, as the building
method forced the next prime to be the smallest available one, not
yet present and not leading to a contradiction.

All odd non-primes are on the first descending diagonal from the left,
and only there.

Many thanks to Jean-Marc Falcoz for his computer skills, to Maximilian
Hasler and Alexandre Wajnberg for their support.

The full 60-lines array is visible there:
http://www.cetteadressecomportecinquantesignes.com/PrimeArray.htm

Best,
É.